z^2-5z=30

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Solution for z^2-5z=30 equation:


Simplifying
z2 + -5z = 30

Reorder the terms:
-5z + z2 = 30

Solving
-5z + z2 = 30

Solving for variable 'z'.

Reorder the terms:
-30 + -5z + z2 = 30 + -30

Combine like terms: 30 + -30 = 0
-30 + -5z + z2 = 0

Begin completing the square.

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + -5z + 30 + z2 = 0 + 30

Reorder the terms:
-30 + 30 + -5z + z2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + -5z + z2 = 0 + 30
-5z + z2 = 0 + 30

Combine like terms: 0 + 30 = 30
-5z + z2 = 30

The z term is -5z.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5z + 6.25 + z2 = 30 + 6.25

Reorder the terms:
6.25 + -5z + z2 = 30 + 6.25

Combine like terms: 30 + 6.25 = 36.25
6.25 + -5z + z2 = 36.25

Factor a perfect square on the left side:
(z + -2.5)(z + -2.5) = 36.25

Calculate the square root of the right side: 6.020797289

Break this problem into two subproblems by setting 
(z + -2.5) equal to 6.020797289 and -6.020797289.

Subproblem 1

z + -2.5 = 6.020797289 Simplifying z + -2.5 = 6.020797289 Reorder the terms: -2.5 + z = 6.020797289 Solving -2.5 + z = 6.020797289 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + z = 6.020797289 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + z = 6.020797289 + 2.5 z = 6.020797289 + 2.5 Combine like terms: 6.020797289 + 2.5 = 8.520797289 z = 8.520797289 Simplifying z = 8.520797289

Subproblem 2

z + -2.5 = -6.020797289 Simplifying z + -2.5 = -6.020797289 Reorder the terms: -2.5 + z = -6.020797289 Solving -2.5 + z = -6.020797289 Solving for variable 'z'. Move all terms containing z to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + z = -6.020797289 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + z = -6.020797289 + 2.5 z = -6.020797289 + 2.5 Combine like terms: -6.020797289 + 2.5 = -3.520797289 z = -3.520797289 Simplifying z = -3.520797289

Solution

The solution to the problem is based on the solutions from the subproblems. z = {8.520797289, -3.520797289}

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